Some Properties of the Fourier-Transform on Semisimple Lie Groups. III

1959 ◽  
Vol 90 (3) ◽  
pp. 431 ◽  
Author(s):  
L. Ehrenpreis ◽  
F. I. Mautner
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Semisimple Lie Groups ◽  
The Fourier Transform

scholarly journals A qualitative uncertainty principle for semisimple Lie groups

1988 ◽  
Vol 45 (1) ◽  
pp. 127-132 ◽  
Author(s):  
Michael Cowling ◽  
John F. Price ◽  
Alladi Sitaram
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Finite Measure ◽  
Semisimple Lie Groups ◽  
Qualitative Uncertainty

AbstractRecently M. Benedicks showed that if a function f ∈ L2(Rd) and its Fourier transform both have supports of finite measure, then f = 0 almot everywhere. In this paper we give a version of this result for all noncompact semisimple connected Lie groups with finite centres.

scholarly journals Hardy Uncertainty Principle for Low Dimensional Nilpotent Lie Groups G4 (III)

1970 ◽  
Vol 6 (1) ◽  
pp. 89-95
Author(s):  
CR Bhatta
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Nilpotent Lie Groups ◽  
Hardy’S Theorem ◽  
Keywords And Phrases ◽  
Engineering And Technology ◽  
The Fourier Transform ◽  
Low Dimensional

An uncertainty principle due to Hardy for Fourier transform pairs on ℜ says that if thefunction f is "very rapidly decreasing", then the Fourier transform can not also be"very rapidly decreasing" unless f is identically zero. In this paper we state and provean analogue of Hardy's theorem for low dimensional nilpotent Lie groups G4.Keywords and phrases: Uncertainty principle; Fourier transform pairs; veryrapidly decreasing; Nilpotent Lie groups.DOI: 10.3126/kuset.v6i1.3315 Kathmandu University Journal of Science, Engineering and Technology Vol.6(1) 2010, pp89-95

scholarly journals Low-dimensional Nilpotent Lie Groups G4

1970 ◽  
Vol 10 ◽  
pp. 155-159
Author(s):  
Chet Raj Bhatta
Keyword(s):  
Fourier Transform ◽  
Key Words ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Science And Technology ◽  
Nilpotent Lie Groups ◽  
The Fourier Transform ◽  
Low Dimensional

An uncertainty principle due to Hardy for Fourier transform pairs on R says that if the function f is "very rapidly decreasing" then the Fourier transform cannot also be "very rapidly decreasing unless f is indentically zero." In this paper we study the relevant data for G4 and state and prove an analogue of Hardy theorem for low-dimensional nilpotent Lie groups G4.Key words: Fourier transform; Uncertainity principle; Nilpotent Lie groupsDOI: 10.3126/njst.v10i0.2951Nepal Journal of Science and Technology Vol. 10, 2009 Page: 155-159 

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